Towards Analysis of Covariance Matrices through Bures-Wasserstein Distance

Towards Analysis of Covariance Matrices through Bures-Wasserstein Distance | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Towards Analysis of Covariance Matrices through Bures-Wasserstein Distance Jingyi Zheng, Huajun Huang, Yuyan Yi, Yuexin Li, Shu-Chin Lin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3911651/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Brain-computer interface (BCI) builds a bridge between human brain and external devices by translating brain signals into commands for devices to perform the user’s imagined action. The core of the BCI system is the classifier that labels the brain signals as the user’s imagined action. Among the array of techniques, those directly classifying covariance matrices using Riemannian geometry find broad applications not only in BCI but also in diverse domains like computer vision and biomedical imaging. However, the existing Riemannian-based methods exhibit limitations, including time-intensive computations, susceptibility to disturbances, and convergence challenges in scenarios involving high-dimensional matrices. In this paper, we tackles these issues by introducing the Bures-Wasserstein (BW) distance for analyzing positive semi-definite matrices. Both theoretical and computational aspects of BW distance are investigated, and three algorithms are proposed to estimate the Fréchet Mean (or barycenter) of a set of matrices efficiently and robustly. The BW distance and barycenter are further integrated into the Minimum Distance to Riemannian Mean classifier to explore their performance in classification tasks. Extensive simulations are conducted to evaluate the effectiveness and robustness of the BW distance and barycenter. Additionally, we showcase the superior classification performance and enhanced computational efficiency of BW distance through evaluations on five real datasets. Biological sciences/Neuroscience/Computational neuroscience/Learning algorithms Biological sciences/Computational biology and bioinformatics/Data mining Health sciences/Health care/Medical imaging/Brain imaging Physical sciences/Engineering/Biomedical engineering Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3911651","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":273819226,"identity":"8f42e605-c386-43ec-81cf-7f9e9bdb72ff","order_by":0,"name":"Jingyi Zheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBACxmYQaQBGDAwfGBgSIOJsRGphnEGMFjgAaWHmIUYLczvv4dc8BQz25uy9h1/b1BzOM7h99gDDh7LDeBzGl2bNY8DAbNlzLs0659jhYoNzeQmMM87h08JjZgzUwmZwI8fMOIftcOKGMzwGzLxthLXwGNx/Y2Zs8Q+q5S9+LcaPgVokDG4AGYxtUC2MBGxhnGMgYWBwJseMsbcvvVgSqOVgz7l0nFoM+88Yf3jzx8be4DiQ8eObdR7fGR7DBz/KrHFraWBgk+JhkACx2SRgogdwqgcCeWDUfPwBYTN/wKdyFIyCUTAKRi4AAGIRUY+6RjndAAAAAElFTkSuQmCC","orcid":"","institution":"Auburn University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jingyi","middleName":"","lastName":"Zheng","suffix":""},{"id":273819227,"identity":"e20084ce-328d-463d-a8de-cc4fa6dbaee3","order_by":1,"name":"Huajun Huang","email":"","orcid":"","institution":"Auburn University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Huajun","middleName":"","lastName":"Huang","suffix":""},{"id":273819228,"identity":"ccd21d48-65f7-454c-86a8-43827407630d","order_by":2,"name":"Yuyan Yi","email":"","orcid":"","institution":"Auburn University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuyan","middleName":"","lastName":"Yi","suffix":""},{"id":273819229,"identity":"b82aaece-7ad3-44ce-aacb-6591bc94616f","order_by":3,"name":"Yuexin Li","email":"","orcid":"","institution":"Auburn University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuexin","middleName":"","lastName":"Li","suffix":""},{"id":273819230,"identity":"80aa09c7-00c9-4b06-809d-a9163b5e2adb","order_by":4,"name":"Shu-Chin Lin","email":"","orcid":"","institution":"National Health Research Institutes","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shu-Chin","middleName":"","lastName":"Lin","suffix":""}],"badges":[],"createdAt":"2024-01-30 20:14:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3911651/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3911651/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80782435,"identity":"b5b3521f-dd71-4ca1-931d-ac11720d15ec","added_by":"auto","created_at":"2025-04-17 05:01:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2647391,"visible":true,"origin":"","legend":"","description":"","filename":"submissionstoScientificReports.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3911651/v1_covered_5ec48908-0bd7-4630-87b7-25f4c0e27bcc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Towards Analysis of Covariance Matrices through Bures-Wasserstein Distance","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3911651/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3911651/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Brain-computer interface (BCI) builds a bridge between human brain and external devices by translating brain signals into commands for devices to perform the user’s imagined action. The core of the BCI system is the classifier that labels the brain signals as the user’s imagined action. Among the array of techniques, those directly classifying covariance matrices using Riemannian geometry find broad applications not only in BCI but also in diverse domains like computer vision and biomedical imaging. However, the existing Riemannian-based methods exhibit limitations, including time-intensive computations, susceptibility to disturbances, and convergence challenges in scenarios involving high-dimensional matrices. In this paper, we tackles these issues by introducing the Bures-Wasserstein (BW) distance for analyzing positive semi-definite matrices. Both theoretical and computational aspects of BW distance are investigated, and three algorithms are proposed to estimate the Fréchet Mean (or barycenter) of a set of matrices efficiently and robustly. 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